Compensation method for thermodilution catheter having an injectate induced thermal effect in a blood flow measurement

ABSTRACT

A catheter for retrograde orientation in a blood flow is used to determine the blood flow rate by thermodilution measurements. The determination of the blood flow rate accommodates injectate induced thermal influences on a dilution thermal sensor, wherein the thermal influences can occur prior to introduction of the injectate into the blood flow.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a division of U.S. Ser. No. 10/079,693 filedFeb. 20, 2002, entitled Compensation Method for Thermodilution Catheterhaving an Injectate Induced Thermal Effect in a Blood Flow Measurementand which is expressly incorporated by reference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with government support under Phase I SBIR(Small Business innovative Research Grant #1 R43 DK55444-01A2 awarded bythe National Institutes of Health. The government has certain rights inthe invention.

REFERENCE TO A “SEQUENCE LISTING”

Not applicable.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to blood flow measurement bythermodilution measurement, and more particularly to compensating for aninjectate induced thermal effect on a thermal sensor in a retrogradecatheter.

2. Description of Related Art

In native A-V fistulae, any stenosis is often located at the arterialportion of the vascular access or A-V shunt. The existence of a stenosisin the vascular access typically requires intervention to restoresufficient flow, or at least reduce the rate of occlusion. A typicalinterventional procedure is angioplasty.

The purpose of the interventional procedures, such as angioplasty, is torestore the flow through the vessel. Interventional radiologists andcardiologists therefore have a need to measure the efficacy of the flowrestoring procedure.

In the angioplasty procedure, an interventional radiologist will inserta sheath (introducer) for the angioplasty balloon catheter facing thestenosis location and thus facing the blood flow in the vessel such asan A-V shunt. It is procedurally convenient to use the same introducer(sheath) for flow measurement. This procedure will locate thethermodilution catheter facing the blood flow and the position, facingthe flow, is termed as “retrograde” position. Also in clinicalsituations such as angioplasty of extremities, it is convenient to reachthe stenosis location from a downstream cannulation site. In all thesesituations, the thermodilution catheter will be facing the flow, andthus in a retrograde position. Yet, there remains a need for determiningthe blood flow rate.

Another situation is related to the endovascular procedure of placementof transjugular intrahepatic portosystemic shunts (TIPS). During theTIPS procedure, a special shunt is created to connect the portal veinwith hepatic vein. The TIPS procedure is usually done to decrease theportal hypertension. However, the amount of blood that is taken by theshunt is unknown. If the amount of blood flow through the shunt is toohigh, then the amount of blood passing through the liver to be filteredis too small, which can result in damage to the patient. Alternatively,if the amount of blood flowing through the shunt and thus shunted fromthe liver, is small, then the effectiveness of the procedure isdiminished. The need exists for determining the blood flow so thatproper treatment can be administered.

Currently, blood flow measurements are performed not during interventionbut later using color Doppler measurements of line velocity, but do notprovide a blood flow measurement in ml/min.

Not withstanding, no practical, relatively quick, and low cost solutionexists in the prior art for determining the relevant flow in theseexample procedures. Therefore, the need exists to measure blood flowusing a catheter introduced into the vessel in retrograde direction. Itis an object of the present invention to provide low cost flowmeasurement methods and devices for such measurements which solve theproblems (and design constrains) of the retrograde thermodilutioncatheter.

BRIEF SUMMARY OF THE INVENTION

The present invention is generally directed to determining blood flowrates, and more particularly to indicator dilution techniques, wherein asignal is introduced into the blood upstream and a downstream dilutionsignal is sensed. Of the indicator dilution methods, thermodilution isapplicable in the present disclosure. In thermodilution measurements, aninjectate (having a different temperature than the blood flow to bedetermined) is introduced at an upstream location and a thermal sensor(or dilution thermal sensor) monitors passage of the injectate at adownstream location.

In a number of configurations, a thermodilution catheter is employed,wherein the catheter includes an injectate lumen for introducing theinjectate into the relevant blood stream and a dilution thermal sensorfor monitoring a downstream passage of the injectate in the bloodstream. The catheter can also include an injectate thermal sensor forproviding a signal corresponding to an injectate temperature prior tointroduction of the injectate into the blood flow.

As a consequence of thermal transfer, such as conduction or radiationwithin the catheter, the dilution thermal sensor in the retrogradecatheter will register temperature changes, or effects, both by theinjectate (indicator) passing through the catheter and the diluted bloodflowing past the catheter. In this case, inside cooling of the dilutionthermal sensor falsely increases the area under the resulting dilutioncurve and thus decreases the accuracy of the measurement.

The present invention also provides for measurement of the blood flowduring the TIPS procedure, wherein the measurements can be convenientlyperformed by a retrograde catheter, introduced for example through thejugular vein, through the vena cava, and through the hepatic vein.

The measurements can be performed before intervention, after the shuntconstruction, in the shunt and in the vena porto (portacaval shunt). Inthis case, the retrograde catheter can be introduced through the hepaticvein, through the shunt and into the vena porta. The advantage of ablood flow measurement during the intervention is the ability to changethe shunt flow if the shunt flow is not adequate.

The present configurations are directed to improving blood flowmeasurement accuracy in thermodilution measurements in a retrogradecatheter by accounting for the presence of the inside cooling effect.The present configurations include (i) the pre-calibration of thethermal conductive properties of the catheter to determine K_(i) over anintended range of operating conditions, wherein the calibration data isused to adjust thermal measurements; (ii) a plurality of injections ofdifferent volumes or different time length from which a cooling effecton the dilution thermal sensor from inside the catheter can bedetermined, and/or an injectate temperature can be calculated; (iii) aplurality of thermal sensors, where the magnitude of the inside coolingeffect on the dilution thermal sensor is measured by an additionalthermal sensor and compensated; (iv) a plurality of pre-calibratedthermal sensors, to simultaneously eliminate the necessity of measuringthe injectate temperature and the inside cooling effect; (v) creatingspecial construction of the retrograde catheter to enhance, or maximizethe thermal isolation of the injectate lumen from the dilution thermalsensor; or (vi) employing any combination of i-v.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)

FIG. 1 is a cross sectional view of an indicator dilution catheterinserted in a vessel in the downstream direction of the blood flow andcurved to reduce sensor contact with the vessel wall.

FIG. 2 is a cross sectional view of an indicator dilution catheterinserted in the vessel in the upstream direction, thus facing the bloodflow.

FIG. 3 is a graphical representation of the relationship between timeand blood temperature by the dilution thermal sensor and measurement ofinjection time.

FIG. 4 is a graphical representation of the relationship between timeand temperature by the injection temperature sensor and measurement ofinjection time, when such injection temperature sensor is located in aportion of the catheter in contact with the blood stream.

FIG. 5 is a graphical representation of the relationship between timeand temperature by the injection temperature sensor and measurement ofinjection time, when such injection temperature sensor is locatedoutside the blood stream and the body of the patient.

FIG. 6 is a graphical representation of a thermodilution curve from thecatheter inserted facing the direction of blood flow (retrograde).

FIG. 7 is a graphical representation of the relationship between insidecooling (K/i, ΔT_(i)) and the speed of the injection.

FIG. 8 is a graphical representation of the relationship between insidecooling (K_(i), ΔT_(i)) and blood velocity.

FIG. 9 a is a graphical representation of a dilution curve, wherein areaS_(c) is approximated as a rectangle S_(c1).

FIG. 9 b is a graphical representation of a dilution curve, where areaS_(c) is approximated by ΔT_(i) and the shape of dilution curve(S_(c2)).

FIG. 9 c is a graphical representation of a dilution curve, where areaS_(c) is approximated by the area S_(c3) under the curve that has thesame shape (similar) as the dilution curve but is proportionally smallerhaving maximum at ΔT_(i).

FIG. 9 d is a graphical representation of a dilution curve, with acontinuous infusion, where the measured temperature shift is H_(m).

FIG. 10 is a cross sectional view of a thermodilution catheter having atwo sensor compensation system with a distal thermal sensor subject toreduced temperature influence of outside dilution [without dead space].

FIG. 11 is a cross sectional view of a thermodilution catheter having atwo sensor compensation system with a distal sensor no influence ofoutside dilution (with dead space).

FIG. 12 is a cross sectional view of a thermodilution catheter with atwo sensor compensation system with different influence of outside andinside cooling on the thermal sensors.

FIG. 13 a is a cross sectional view of a thermodilution catheter withthe thermal sensor spaced from an injectate channel and injection port.

FIG. 13 b is a cross sectional view taken along lines 13 b-13 b of FIG.13 a.

FIG. 14 a is a cross sectional view of a thermodilution catheter withthe inclusion of the air gap between the dilution thermal sensor and theinjectate channel, and the injectate thermal sensor located inside theair gap channel.

FIG. 14 b is a cross sectional view taken along lines 14 b-14 b of FIG.14 a.

FIG. 15 a is a cross sectional view of a thermodilution catheter whereboth thermal sensors are located in one lumen, with an air gap betweenthe dilution thermal sensor and the injectate lumen and a closed air gap(thermal conductor) between the injectate thermal sensor and theinjectate lumen.

FIG. 15 b is a cross sectional view taken along lines 15 b-15 b of FIG.15 a.

FIG. 16 is a cross sectional view of a thermodilution catheter with theinjectate thermal sensor placed in at least one of the manifold, theinjection side arm, the injection sides arm or the catheter so that thethermal sensor is separable from the catheter.

FIG. 17 is a cross sectional view of a thermodilution catheter with thenarrowing at the tip of the injectate lumen, such as a guide wire portin a guide wire lumen.

DETAILED DESCRIPTION OF THE INVENTION

Referring to FIGS. 1 and 2, the present indicator dilution catheter 10is shown operably located in an arterio-venous (A-V) shunt 12. The A-Vshunt 12 has a blood flow shown by the direction of the arrows, thecatheter 10 includes an elongate body 20 having an extravascular portion22 and an intravascular portion 24. The extravascular portion 22 beingthat portion or length of the body 20 that is not operably locatedwithin the A-V shunt 12 to contact the blood flow in the shunt. Theintravascular portion 24 is that portion or length of the body 20 thatis operably located within the A-V shunt 12 and contacts the blood flowin the shunt. The body 20 includes a proximal end, a distal end 28, anindicator (injectate) lumen 32, an injection port(s) 34 and a dilutionsensor 36 for detecting passage of the injected indicator in the bloodflow in the A-V shunt 12. That is, the dilution sensor measures atemperature of the diluted blood flow resulting from introduction of theinjectate into the blood flow. Typically, the catheter 10 is operablyconnected to, or connectable to a controller. The controller can be adedicated unit including hardware and software.

In operation, the indicator passes along the catheter 10 through theinjectate lumen 32 to be introduced into the A-V shunt 12 blood flowthrough the injection port 34. The dilution sensor 36 is typicallyconnected to the controller via a lead or wire extending along thecatheter 10.

It is important for the dilution sensor 36 inside the blood stream toavoid contact with the A-V shunt wall or influence of the A-V shuntwall. To reduce the likelihood of the dilution sensor 36 touching thewall, a special curvature of the catheter 10 as seen in FIG. 1 can beused. This curvature is selected to reduce the potential for contactbetween the dilution sensor 36 and the A-V shunt wall. A length of theintravascular portion 24 of the body 20, and typically a length proximalto the distal end 28 of the body includes an inclined spacing section44. The spacing section 44 has a longitudinal axis S-S that is nonco-linear and non parallel to the longitudinal axis IP of an adjacentsection of the intravascular portion 24. That is, the longitudinal axisof the spacing section 44 intersects the longitudinal axis of theadjacent section of the intravascular portion 24.

As the preferred configuration of the catheter 10 is directed tothermodilution, the dilution sensor 36 is a thermal sensor such as athermistor. Preferably, the dilution sensor 36 has as small a volume aspossible, so that the cross sectional area of the catheter 10 can beeffectively minimized. However, it is understood the thermal sensor 36can be any sensor that can measure temperature, for example, but notlimited to thermistor, thermocouple, electrical impedance sensor(electrical impedance of blood changes with temperature change),ultrasound velocity sensor (blood ultrasound velocity changes withtemperature), blood density sensor and analogous devices. In fact, anyparameter of blood that changes with temperature can be used to obtainthermodilution measurements.

However, the present invention is particularly applicable to thosethermal sensors having a performance that is temperature dependence.That is, those sensors that are effected by induced temperaturefluctuations from exposure to a cooled or heated injectate (indicator)passing through the catheter. Temperature sensors are suited to thepresent invention, as the temperature of the sensor (and hence recordedtemperature) can be effected by cooling or heating from the injectateprior to introduction of the injectate into the flow to be measured.

The dilution sensors 36 detect a blood parameter and particularlyvariations of a blood parameter. For example, the dilution sensors 36may be electrical impedance sensors, or optical sensors, the particularsensors being dependent on the blood characteristics of interest.Ultrasound velocity sensors, as well as temperature sensors and opticaldensity, density or electrical impedance sensors can be used to detectchanges in blood parameters. The operating parameters of the particularsystem will substantially dictate the specific design characteristics ofthe dilution sensor 36, such as the particular sound velocity sensor. Ifa plurality of dilution sensors 36 is employed, the sensors can beidentical components. Ultrasonic sensors measure sound velocity dilutionas the indicator material is carried past the sensor by the bloodstream,and changes in sound velocity are plotted to permit calculation ofvarious blood parameters. The time at which the indicator material(injectate) reaches the sensor 36 after injection, the area under theplotted curve representing the changes in sound velocity at the sensor,and the amplitude of the measurement all provide information concerningthe blood flow.

The indicator includes, but is not limited to any of the knownindicators including a temperature gradient indicator, such as a bolusof a continuous injection.

Preferably, the indicator is injectable through the injection port 34and is thus an injectate. The injected (or introduced) indicator,injectate, thus forms an indicator bolus.

The injected indicator, a liquid, can be a solution that is preferablynon detrimental or minimizes any detriment to the patient, the blood ofthe patient, any blood components, including blood, and is non-reactivewith the material of the system, including the material of A-V shunt. Apreferred indicator is a solution such as isotonic saline and dextrose(glucose). However, it is understood any of a variety of solutions canbe employed. Further, the term solution is taken to include singlecomponent injections. For thermodilution measurements, the injectate hasa different temperature than the blood flow into which the injectate isintroduced.

The present analysis is set forth in terms of a reduced temperatureindicator, such as an injectate. That is, the indicator has atemperature below the temperature of the blood flow to be measured.However, it is understood that an elevated temperature indicator can beemployed. That is, a temperature that is above the temperature of theblood flow to be measured.

The present invention provides for the determination of a volumetricflow rate (“flow rate”) in an A-V shunt 12. The volumetric flow rate isa measure of the volume of liquid passing a cross-sectional area of theconduit per unit time, and may be expressed in units such as millilitersper min (ml/min) or liters per minute (l/min). A liquid flow having aflow rate also has a flow velocity, the distance traveled in a giventime, such as millimeters per second (mm/s). Thus, for liquid flowing inan A-V shunt, there will be a flow rate (volumetric flow rate) having aflow velocity.

Blood flow rate (Q) can measured by thermodilution, using an indicatorhaving a different temperature than the blood (typically through aninjection of a liquid indicator (injectate)), wherein the blood flowrate Q can be presented by the following formula:Q=k(T _(b) −T _(i))V/S  (Equation 1)

where T_(b) is blood temperature in the vessel prior to injection; Ti isthe temperature of the injectate prior to it entering the blood stream;V [ml] is the volume of injected indicator (injectate); S [temp*time] isthe area under the temperature versus time dilution curve resulting fromthe mixing of the injected indicator (injectate) and the blood; and k isa coefficient related to thermal capacity of blood and the injectedindicator (injectate). Typically, k is taken to be 1.08.

For continuous injections in Equation 1, V [ml/time] is the speed (rate)of the continuous injection, S [temp] is the temperature change of theblood due to mixing with the indicator, wherein the indicator can becolder/warmer than the blood.

A major difference between the classic dilution measurements of cardiacoutput and the measurements of blood flow rate in A-V shunts 12, whereinthe indicator is introduced and a corresponding measurement is takenwithin a given section of the A-V shunt, is the absence of a mixingchamber such as the heart. That is, in classic dilution measurements ofcardiac output, the blood and the indicator flow through the heart,which sufficiently mixes the indicator (thermal change) with the bloodto provide reliable measurements.

However, if the blood and the indicator do not travel through a mixingchamber such as the heart, the design of the measurement system mustprovide for adequate mixing of the indicator with the blood within thespace between the indicator introduction (injection) and the site ofresulting dilution measurement.

The adequacy of mixing can be judged by comparing results of thedilution measurement with a more accurate method like, for example,volumetric timed collection of flow on the bench. If other sources oferrors are controlled, the discrepancy between the measurement resultscan be attributed to inadequate mixing conditions.

Whether the mixing is adequate depends on the requirements of theclinical users and the dynamic range of the measured parameters. Forexample, for an angioplasty restoring procedure in A-V lower arm shunts,an average increase of the blood flow after angioplasty procedure isapproximately 300-400 ml/min from 400-600 ml/min to 700-1000 ml/min. Ameasurement method would reliably indicate such procedural changes inflow, if its absolute error of flow measurement is less than the largerof 60-100 ml/min or 10%.

There are two different orientations for catheter placement in the A-Vshunt 12. The A-V shunt 12 normally has a single flow direction, whereinblood flows from the arterial (upstream) side to the venous (downstream)side. Thus, the term downstream indicates directed with the flow, andthe term upstream indicates directed against the flow.

1. Referring to FIG. 1, a catheter 10 is placed in the direction ofblood flow, pointing downstream. In this case, the injected indicatorenters the blood flow from a point along the catheter 10, or upstream ofthe catheter, and the dilution temperature change can be recorded by thedilution sensor 36 at or near the distal end 28 of the catheter 10.

2. Referring to FIG. 2, the catheter 10 is placed facing the blood flow,pointing upstream (the retrograde position or configuration). In thiscase, if the injected indicator is introduced in the blood flow of theA-V shunt via the same catheter, the indicator will first travel pastthe dilution sensor 36 as the indicator passes along the indicator lumen32.

To enhance the accuracy of the measurements of blood flow rates usingthermodilution, the following problems associated with specifics ofthermodilution blood flow measurement within the A-V shunt 12 should beaddressed:

(i) Supporting mixing conditions; and

(ii) Reducing measurement errors resulting from the introduction of anindicator.

(i) Supporting Mixing Conditions

Various mechanisms can be implemented for enhancing the mixingconditions within the A-V shunt 12:

(a) Plurality of injection sites To create a uniform indicatordistribution throughout the cross section of the flow in the A-V shunt12, a plurality (two or more) of injection ports 34 for indicatorintroduction can be used. These injection ports 34 can be located on thesame level or at different levels within, or across the cross sectionalprofile of the A-V shunt. These injection ports 34 can be located toface the flow, be with the flow or have spiral form or other forms,locations and configurations. It is preferable that the indicator passthrough the catheter 10 in a single lumen or channel 32, from which theindicator is distributed to the plurality of injection ports 34. FIG. 1depicts multiple configurations of arrays for the injection ports 34. Itis understood a single array of injection ports would be employed in acatheter, and the multiple arrays in FIG. 1 are for illustrationpurposes. In FIG. 2, two locations of the injection port 34 (single portor in array form) are shown, again with the understanding a singleconfiguration is employed in a given catheter 10. Specifically, theinjection port 34 can be at the distal end 28 or proximal to the distalend.

(b) Plurality of dilution sensors To increase the accuracy of themeasurements, especially in conditions where desired mixing may bedifficult to achieve, a plurality of dilution thermal sensors 36 can beused. The plurality of dilution thermal sensors 36 are particularlyapplicable in conjunction with catheters having one port, a pluralityports, or a non volume indicator introduction such as the heating orcooling of the blood. In addition, a plurality of dilution sensors 36can be employed when the indicator is introduced through a separateintroducer, rather than the catheter on which the dilution sensors arelocated. Further, corresponding to the graph of FIG. 5 and seen in FIGS.1 and 2, a sensor 36 a can be located outside the A-V shunt 12 toprovide the measurement of the passage of the indicator through theshunt. The flow rate Q_(c) may be calculated from the individualdilution sensor measurement Q1, Q2, Q3, . . . for example, as follows.If the sensors are disposed, about a circle or ring, simple averagingcan be performed: $\begin{matrix}{Q_{c} = \frac{( {Q_{1} + Q_{2} + Q_{3} + {\ldots\quad Q_{n}}} )}{n}} & ( {{Equation}\quad 2} )\end{matrix}$

where n is the number of sensors. Alternatively, the area under thedilution curve associated with each sensor can be summed and averagedfor determining the flow. As a further refinement, one could evaluateall individual sensor readings and discard one if its measurementindicates that the sensor is positioned against the vessel wall.

(c) Turbulent introduction of the indicator into the blood flow in theA-V shunt. The kinetic energy introduced into the initial blood flow Qby the injected indicator can enhance the mixing conditions by creatingturbulence in the blood flow. This can be achieved by making theopening(s) 34 in the catheter 10 from where the indicator leaves thecatheter and enters the blood stream sufficiently small so the indicatorwill “jet” into the flow at a higher velocity than the present bloodvelocity. The turbulence may be enhanced by angling these holes so theinjection jet is directed against the direction of blood flow in the A-Vshunt 12. The turbulence may be enhanced by the use of a plurality ofholes spaced around the perimeter of the catheter, such as along a ring.However, for the jetting introduction, the injection ports 34 are sizedto at least substantially preclude hemolysis in the A-V shunt 12.

(d) Use of a thermally conductive band. Placing a thermally conductiveband 48 around the catheter at the site of the indicator dilution sensor36 and in close thermal contact with the sensor. Such a band, typicallyconstructed of metal, will assure that the dilution sensor 36 willaverage the temperatures of a larger cross sectional area of the bloodflow, and will thus partly offset variations in blood temperature thatresult from inadequate mixing. As the sensing will be done around thefull perimeter of the catheter 10, such a band 48 will also reduce theloss in measurement accuracy that results when an un-banded indicatordilution sensor is positioned against the wall of the A-V shunt 12.

The distance between the injection port 34 and the dilution thermalsensor 36 are preferably selected to provide sufficient mixing of theintroduced indicator and the blood. For the catheter 10 facing the flow,the distance between the port 34 and the sensor 36 is approximately 2 to4 cm. For the catheter 10 oriented with the flow, the distance betweenthe injection port 34 and the sensor 36 is approximately 3 to 6 cm.

(ii) Reduce Measurement Errors Resulting from the Introduction of anIndicator.

The introduction of a volume of indicator at a flow rate Q_(i) canchange the initial flow rate Q. The effect of Q_(i) depends on theparticulars of the hemodynamic resistance of the A-V shunt 12.

In the arterial environments, the major resistance to flow is downstreamwhere the downstream resistance may well exceed the upstream resistance20-100-fold. Thus, the injected flow does not change the initial flow atthe site of the sensor. During the injection period, the arterial inflowinto the measurement site will temporarily reduce in response to theintroduced injection. In this case, the recorded dilution curve willrepresent the initial blood flow rate, and the measured blood flow rateQ_(m) will be close to initial blood flow:Q_(m)=Q  (Equation 3)

In the venous environments, the main flow resistance is upstream fromthe measuring site, where the flow resistance may exceed the downstreamflow resistance 20-100-fold. In this situation, the dilution measurementQ_(m) will represent the sum of initial flow and injected flow:Q _(m) =Q+Q _(i).  (Equation 4)

In A-V shunt systems 12 the location and distribution of the resistancesis unknown. That is, the resistance to flow can be downstream in whichthe volume of the introduced indicator will effectively not be seen.Alternatively, the resistance to the flow in the A-V shunt 12 can beupstream, in which case the measured flow will include at least aportion of the flow rate of the introduced indicator. In the A-V shunt12, the flow resistances will depend on factors such as initial surgicalanatomical construction of the shunt, locations of stenoses andplacement of the catheter. Thus, contrary to the arterial and venousenvironment, the relationship of the measured flow rate Q_(m) in A-Vshunts to initial blood flow rate is unknown. The measured flow rateQ_(m) will be somewhere between initial flow Q and the initial flow plusinjection flow Q+Q_(i), depending on distribution of resistances inrelation to the place of the injection. The range of uncertaintydirectly depends on the injection flow rate Q_(i). Therefore, while alarger Q_(i), is desirable for enhancing mixing conditions, therelatively large Q_(i) may result in a less accurate flow measurementbecause of the unknown effect of Q_(i) on the initial flow rate. Thebest flow rate Q_(i) is a compromise: not too large, not too small. Tominimize the error from the injection flow rate Q_(i) being too large ortoo small, the following can be employed:

1. Calculating the flow rate Q_(c) based on the injection flow rateQ_(i) and on information of measurement conditions such as the type ofthe A-V shunt, the distribution of the resistances and the value ofQ_(m) itself.

2. Limiting the ability of operator to inject the indicator too quickly,while still providing sufficient ejection velocity to enhance mixing.

3. Rejecting the result of the flow measurement Q_(m), if the flow rateof the injection Q_(i) is too high or too low.

4. Employing two injection flow rates to gain a further improvement inshunt flow measurement accuracy and to reveal the location of thehemodynamically significant stenosis in the A-V shunt.

1. Calculating Q_(c) by Adjustment of the Measured Value of Q_(m)

In high-flow, well developed native fistula, the major flow resistance(between 50% and 100%) is located at the arterial anastomosis. Thismeans that the flow resistance downstream from the injection is between0 and 50% of the total flow resistance. For this case the flowmeasurement error is reduced by using a flow calculation algorithm,which places 75% of the flow resistance upstream from the point ofindicator introduction, 25% downstream. The calculated flow Q_(c) willthen beQ _(c) =Q _(m)−0.75Q _(i)  (Equation 5)

In this case the possible error introduced by the injection flow will beless than 25% of Q_(i).

In most well functioning lower arm artificial grafts, blood flow is inthe range of 1000-1600 ml/min. The literature suggests again that themajor flow resistance (between 50% and 100%) is located upstream fromthe catheter (arterial anastamosis, supplying artery). Therefore,equation 5 can be used.

Therefore, if the indicator dilution measurement of shunt flow is1100-1200 ml/min or more the flow measurement device or controller maybe configured to automatically use Equation 5.

On the other hand, flow limiting stenoses in artificial grafts generallydevelop in the venous outflow side of the A-V shunt. Therefore, if theangiogram reveals that such is the case, another measurement algorithmfor such specific instances can be used. Assuming that at least 50% ofthe flow resistance is now on the venous side, the algorithm could nowbe:Q _(c) =Q _(m)−0.25Q _(i)  (Equation 6)

In this case the possible error introduced by the injection flow willagain be less than 25% of Q_(i).

In the general case when the distribution of hemodynamic resistances isunknown, one may minimize influence of injection flow on the flowreading reported to the operator through the use the following equationto calculate initial flow Q_(c): $\begin{matrix}{Q = {Q_{m} - \frac{Q_{i}}{2}}} & ( {{Equation}\quad 7} )\end{matrix}$

In this case the error from the injected flow will be less than 50% ofQ_(i).

The value of Q_(i) can be estimated, for example, as a ratio of knowninjected indicator volume (V) and time of injection (t): $\begin{matrix}{Q_{i} = \frac{V}{t}} & ( {{Equation}\quad 8} )\end{matrix}$

wherein the time of injection t can be estimated from the temperaturecurve of a thermal sensor. For example, the time t can be derived fromthe indicator dilution curve, from the width of that curve at its halfheight (FIG. 3), or from the time period between the beginning the bolusregistration to the moment to the beginning of the downslope.Alternately, the time t can be derived from the curve from the injectionthermal sensor by the time period between the beginning of the bolus tothe beginning of the downslope (FIG. 4 and FIG. 5). Alternatively, if adedicated indicator injection pump is used, the value of the injectiontime can be acquired from the pump setting.

2. Limiting the Ability of the Operator to Introduce the Indicator TooQuickly

In practice, it is important to limit the ability of the operator toinject the indicator too quickly, thus introducing large flow changes.For example, in [Ganz 1964] the authors injected 5 ml of saline in0.3-0.5 second, which results in an injected flow rate of Qi=600-1000ml/min. This injected flow rate is unacceptable in A-V shunt flowmeasurements because the injected flow rate may exceed the actual flowin the shunt, thereby introducing large error. Thus, the speed of theindicator injection is a compromise between the need to achievesufficient mixing (the higher injection flow the better chance ofsufficient mixing) and the need to limit the flow rate of the indicatorinjection because of increase in error due to unknown distribution ofresistances.

To limit the ability to inject too quickly, the indicator lumen 32and/or injection port(s) 34 can be designed to be sufficiently small toincrease the resistance to flow. That is, flow resistance of theindicator through the indicator lumen or the injection ports is selectedto limit the injection rate.

For example the indicator lumen or the flow path of the indicator caninclude a tortuous flow path 52 which provides sufficient resistance toflow to preclude a injection flow rate greater than 200 ml/min. In apreferred configuration, the injection rate is between approximately 60ml/min to 200 ml/min. The resistance is selected to provide the desiredflow rate for, or within, normal anticipated pressures on the indicator.Also, the indicator may pass through a cellular structure 54 to createthe desired flow resistance. It is also contemplated the injectionport(s) 34 can be sized to create at least a portion of the flowresistance to limit the upper end of the indicator injection flow rate.In a preferred embodiment, the injection ports 34 of the catheter 10 maybe dimensioned to serve this function.

As an alternate, flow-limitations may be programmed into an automatedpump that provides controlled indicator injections. This pump can beprogrammed to repeat measurements if the pump rate is improper based onthe measured rate of shunt flow, and repeat such measurements at a moreoptimal rate of pump flow.

3. Rejecting the Result of the Flow Measurement If the Injection FlowRate is Too High or Too Small

The rejection of the flow measurement if the introduced indicator flowrate is too small or too large can be accomplished by the controlleroperably connected to the sensor 36. The controller can include softwarefor determining the length of time of the indicator injection andsubsequently reject the measured flow rate, if the indicator flow ratewas too great or too small. The controller can be configured to estimatean indicator injection rate, or rely upon an absolute time t of theinjection. For example, if the 10 ml injection time t is less than 2seconds (Qi>300 ml/min), the controller can reject the resultingmeasured flow rate. Further, if the if the injection time t is greaterthan 10 seconds (Qi<60 ml/min), the controller can reject the resultingmeasurement as the desired mixing may not have been achieved. Suchcontroller may be structured to provide error warnings to the operator.

The window of injection times accepted by the controller can be selectedto automatically take into account the A-V shunt flow reading. Forinstance, if the indicator dilution reading would be 2000 ml/min, aninjection flow rate of 300 ml/min may still be acceptable. If theindicator dilution reading would be only 400 ml/min, the same 300 ml/mininjection rate could create unacceptable measurement tolerances and anoperator warning could be issued to redo the measurement at a slowerinjection rate.

4. Employing Two Injection Flowrates.

Two successive indicator dilution measurements performed at differentinjection flow rates can be made to further increase the A-V shunt flowmeasurement accuracy and/or gain knowledge on whether the flow limitingstenosis in the shunt is located on the arterial or on the venous sideof the shunt.

Analogous to equations 5-8, two injections with different injection flowrate Q_(i1) and Q_(i2) will produce two measured flow rates Q_(m1) andQ_(m2):Q=Q _(m1) −pQ _(i1)  (Equation 9)Q=Q _(m2) −pQ _(i2)  (Equation 10)

where p is the portion of injection flow that adds to the initial flowand should be subtracted from measured flow.

Equations 9 and 10 can be solved for the two unknowns p and the initialshunt flow Q: $\begin{matrix}{Q = \frac{( {{Q_{m1} \times Q_{i2}} - {Q_{m2} \times Q_{i1}}} )}{( {Q_{i2} - Q_{i1}} )}} & ( {{Equation}\quad 11} ) \\{p = \frac{( {Q_{m1} - Q_{m2}} )}{( {Q_{i1} - Q_{i2}} )}} & ( {{Equation}\quad 12} )\end{matrix}$

For accurate measurement of p and Q using Equations 11 and 12, thedifference between the two injection rates, (Q_(i2)−Q_(i1)), should beas large as possible. That is, if Q_(i2) and Q_(i1) approach each other,the numerator becomes too large and thus introduces an unacceptableamount of error into the calculation.

Both indicator introductions, or one of them may be performed from thesame catheter where dilution sensor(s) is (are) located, or throughanother catheter or through the introducer, or through a needle.Injections of different rates also can be done by the dedicated pump. Inone embodiment, a slow injection can be performed through the catheterwhere flow is restricted, a quick injection can be performed through theintroducer of this catheter (the “sheath”). One may also use a catheterwith two separate channels (lumens) with different resistances forinjection at different flow rate. Alternatively, one can use a catheterwith one injection lumen, where the injection into this lumen takesplace via a flow restricting valve with at least two positions.

In instances where it is impractical to inject at two flow rates thatare sufficiently different to yield accurate values for Q and p inEquations 11 and 12, the two-injection method can still be used toeliminate some of the influence of the injection flow rate on themeasurement and thus improve measurement accuracy. In this instance, onewould only employ Equation 12 to find a rough estimation of the value p.If p is well below 50% one can conclude that the main flow resistance islocated in the shunt downstream from the injection port(s). Therefore,the use of Equation 6 is indicated to calculate shunt flow Q_(c); oneshould then calculate Q_(c) using the indicator dilution measurementdone at the lower injection flow rate. Conversely, if p is found to besubstantially larger than 50%, the main flow resistance is likelylocated in the shunt upstream from the injection port(s). In thisinstance the use of Equation 5 is indicated for calculating Q_(c) (againusing the indicator dilution measurement made at the lower injectionflow rate). If p is found to be near 50%, an intermediate injection flowcorrection (Q_(c)=Q_(m)−0.5Q_(i)) is appropriately used. In all theseinstances, the error introduced into the measurement of Q stemming fromthe injection flow is reduced to 25% of the injection flow.

The measurement of p in the above approach yields further information,helping the radiologist to select appropriate corrective procedures. Asdisclosed above, the value of p reveals whether the flow limitingstenosis is located upstream or downstream from the catheter's flowmeasurement site. It therefore informs the radiologist at which side ofthe shuns he/she should perform the flow-restoring procedure. At a smallvalue of p and low shunt flow, the hemodynamically significant stenosisis located at the venous side of the shunt; for a large value of p andsmall shunt flow it is located at the arterial end.

Although the family of inventions disclosed herein is primarilydescribed on the basis of a thermodilution catheter, the spirit ofinvention and equations 2-12 can be used for any dilution catheter.Further, the application need not be limited only to A-V shunts, but canbe employed in any vessel, conduit or channel, where the amount of flowresistance and/or the location of the flow resistance in the flow path(relative to the injection site) is unknown. The flow measurement Q_(m)can be made using any indicator dilution method without departing fromthe spirit of this invention. Measurement or determination of theinjection flow Q_(i) can be calculated from any dilution curve like(FIG. 3); from the measurement the signal of an injection sensor; from adedicated indicator injection pump setting, or simply by dividing thevolume of indicator as indicated on the injection syringe by theinjection time as measured by stopwatch, or any other method know in theart. The calculated flow Q_(c) can be determined from a flow measured byany method known in the art, and the exact correction factor used forQ_(i) in such a calculation can vary between 0 to 100% using withoutdeparting from the spirit of this invention. That is, Q_(m) can bedetermined by any methodology, formula or derivation, whereupon thepresent invention of determining Q_(c) can be performed by modifying themeasured flow Q_(m). It is also understood the dilution measurements canbe made percutaneous. That is, the sensors 36 a can be located outsideof the vessel or shunt 12 to measure the indicator in the flow withinthe shunt, wherein the resulting measured flow can be modified by thepresent formulas and concepts. Thus, the sensors 36, 36 a can beoptical, electrical, impedance, ultrasound or other sensor that canprovide measurements of the indicator within the shunt 12percutaneously.

When the thermodilution measurements are performed with the catheterfacing the blood flow (in the retrograde position), as seen in FIG. 2,the injected indicator (injectate) will cool the dilution thermal sensor36 through the catheter walls while passing within the catheter to thedistal part (tip part) of the catheter 10. Thus, when the diluted cooledblood contacts the dilution thermal sensor 36, the dilution thermalsensor will already be cooled to some degree by the internal passage ofthe indicator, and the signal from the thermal dilution sensor will bethus influenced by both the cooling energy from the inside the catheter10 and the cooling energy from the diluted outside blood flow (the bloodflow in the vessel). The dilution sensor is that sensor which senses thetemperature of the diluted blood flow in the conduit.

The cooling of the dilution thermal sensor resulting from the indicator(injectate) flowing through the injection (injectate) lumen 32 willhereafter sometimes be referred to as the “inside cooling” and the“inside cooling effect”. The inside cooling effect can introduce asignificant error by a spurious increase in the area under dilutioncurve seen in the blood flow measurement (FIG. 6 area S_(c)).

The injectate thus creates a measurement (or signal) offset in thedilution sensor. That is, the dilution sensor would provide a differentmeasurement or signal in the absence of the injectate travelling throughthe catheter (prior to introduction) into the blood stream. Typically,this measurement offset is a change in the temperature of the dilutionsensor resulting from thermal exposure of the dilution sensor to theinjectate in the catheter.

The blood flow rate (Q_(f)) measured by the retrograde thermodilutioncatheter (facing the blood flow) will be: $\begin{matrix}{Q_{f} = {\frac{{kV}( {T_{b} - T_{i}} )}{( {S_{m} - S_{c}} )} - Q_{i}^{*}}} & ( {{Equation}\quad 13} )\end{matrix}$

where S_(m)—is the total area under dilution curve; S_(c)—is the portionof the area under dilution curve related to the inside cooling effect,Q_(i)* adjustments for injection flow Q_(i). The Q_(i)* correction termmay be omitted in cases where it is a negligible portion of Q_(f) andthis term is not entered in later equations derived here from Equation13. Nevertheless, those later equations should be read to include theQ_(i)* correction term in cases where added measurement accuracy isdesired.

The theory and the experiments show that the inside cooling effect thatproduces the temperature change ΔT_(i) of the dilution sensor 36 (seealso area S_(c) FIG. 6) can be conveniently characterized through athermal transfer coefficient K_(i). The thermal transfer coefficientK_(i) characterizes the relationship of the measured temperaturedifference between the blood and the injectate (injected indicator) andthe temperature change ΔT_(i) of the dilution sensor: $\begin{matrix}{{{{\Delta\quad T_{i}} = {K_{i}( {T_{b} - T_{i}} )}};}{or}} & {{Equation}\quad 14a} \\{{K_{i} = \frac{\Delta\quad T_{i}}{( {T_{b} - T_{i}} )}};} & {{Equation}\quad 14b}\end{matrix}$

where K_(i) depends on the geometry, the material properties of thecatheter, the flow rate of the injectate injection and the blood flowvelocity in the vessel; T_(b) is the temperature of the blood flow,T_(i) is the temperature of the injectate; and ΔT_(i) is the change inthe dilution sensor temperature resulting from inside cooling by theinjectate.

At a constant temperature difference (T_(b)−T_(i)) the value of K_(i) isfound to be dependent on the speed of the indicator injection (FIG. 7).For a particular 6 French catheter, it has been found that K_(i) becomespractically independent from speed of injection (part 11 in FIG. 7),when the flow rate of indicator injection exceeded 30-40 ml/min. It isunderstood that in other catheter constructions, the value of flow atwhich K_(i) becomes independent of the rate of injection can bedifferent.

The pre calibration of a particular catheter or catheter style tominimize the effect of injectate induced temperature offset of atemperature dilution sensor can be accomplished by differentcoefficients and different procedures, wherein different equations canbe derived, including equations corresponding to the equations setforth.

For example, the relationship of FIGS. 7 and 8 are illustrative anddifferent relationships are possible. Thus, the calibration coefficientcan be selected based upon estimated blood flow (velocity), and hencefor a high blood flow, a smaller K_(i) can be selected, and for a lowerblood flow, a larger K_(i) can be selected. Similarly, an injection ratethat is measured (or determined from an injection curve or a dilutioncurve) can be the basis of a corresponding coefficient. It is understoodthe calibration coefficient can be adjusted in response to the bloodflow rate or the injection rate of the injectate. That is, an initialcalibration coefficient can be determined or estimated, wherein theinitial calibration coefficient is modified in response to feedback fromthe actual flow or injection conditions. For example, if the blood flowrate is less than anticipated, the calibration coefficient can beincreased. Conversely, if the blood flow rate is greater thananticipated, the calibration coefficient can be correspondinglydecreased. These adjustments of the calibration coefficient in responseto feedback from the actual system allows further increase in theaccuracy of the measurements.

At a constant temperature difference (T_(b)−T_(i)) the value of K_(i) isfound to be dependent on the blood flow velocity (FIG. 8). For theparticular 6 French catheter type, the value of K_(i), becomespractically independent from blood velocity (part II of the curve) at25-30 m/sec.

It is understood that in different catheter constructions, the value ofthe blood flow velocity when measurements become independent ofinjection speed may be different.

The shape of the curve that forms the area under the dilution curveS_(c) (FIG. 6) is unknown for bolus injections. It can be expressed bydifferent approximations (FIG. 9 a, FIG. 9 b, FIG. 9 c) based onmeasured dilution curve parameters and a pre-calibrated value of ΔT_(i).For effectively continuous injections, the resulting dilution curve isshown in FIG. 9 d.

For a rectangular approximation (FIG. 9 a), the value for S_(c) can beexpressed:S _(c1) =ΔT _(i) ×t  Equation 15a

where t—is the duration of the injection (for example, the time width ofthe curve at the half height (FIG. 3).

From Equation 14a and Equation 15a:S _(c1) =K _(i)×(T _(b) −T _(i))×t  Equation 15b

The value K_(i) can be precalibrated for any particular catheter fordifferent injection flow rates and for different, blood flow velocitiesin the blood flow to be measured. As it is clear from FIG. 7 and FIG. 8,the proper value of K_(i) can then be substituted in Equation 15b duringactual blood flow measurements based on the actual observed differentflow conditions.

The second possible approximation of S_(c) is the area S_(c2) (FIG. 9b), that is limited by ΔT_(i) and actual shape of dilution curve.

The third possible approximation of S_(c) is the area S_(c3) (FIG. 9 c)that has a similar shape as the actual dilution curve but isproportionally smaller with its maximum at ΔT_(i): $\begin{matrix}{S_{c3} = {S_{m}( \frac{\Delta\quad T_{i}}{A_{m}} )}} & {{Equation}\quad 16}\end{matrix}$

where A_(m) is the maximum of actual measured dilution curve (FIG. 9 c).

In a further refinement, one could mathematically combine the calculatedvalues of S_(c1), S_(c2) and S_(c3) to produce an actual value of S_(c)that provides an optimal blood flow measurement accuracy. For example,the actual value of S_(c) can be considered as an average of S_(c3) andS_(c2): $S_{c} = \frac{( {S_{c2} + S_{c3}} )}{2}$

It is understood different approximations and different combinations ofthe approximation presented above and others can be used to estimateS_(c) for use in Equation 13.

Referring to FIG. 9 d it is also recognized the introduction of theinjectate can effectively be continuous, whereupon the difference inareas under the curves can be obtained by subtracting the measuredtemperature.

In the case of continuous infusion of the indicator, Equation 13 may berewritten as: $\begin{matrix}{Q_{f} = {\frac{{kq}( {T_{b} - T_{i}} )}{( {H_{m} - {\Delta\quad T_{i}}} )} - Q_{i}^{*}}} & ( {{Equation}\quad 13a} )\end{matrix}$

where q—rate of indicator infusion in ml/min; H_(m)—is the total changein the temperature; ΔT_(i)—is the portion of the change related to theinside cooling effect (FIG. 9 d), Q_(i)* adjustments for injection flowQ_(i).

The above and other theoretical and experimental observations show thatthe following primary ways can be used to improve blood flow measurementaccuracy of the retrograde catheter in the presence of the insidecooling effect:

1. Pre-calibration of the thermal conductive properties of the catheterto determine K_(i) over the range of user conditions, and use of thisdata to adjust recorded signals from the thermal sensors;

2. A plurality of injections of different volumes or different timelength from which the inside cooling effect on the dilution thermalsensor and/or the injectate temperature can be calculated;

3. A plurality of thermal sensors, where the magnitude of the insidecooling effect on the dilution thermal sensor is measured by anadditional thermal sensor and compensated;

4. A plurality of pre calibrated thermal sensors, are used tosimultaneously eliminate the necessity of measuring the injectatetemperature and the effect of inside cooling.

5. Creating special construction of the catheter that will enhance ormaximize the thermal isolation of the injectate lumen from the dilutionthermal sensor;

6. Any combination of the above.

1. Pre-Calibration of the Thermal Conductive Properties of the Catheterto Determine K_(i) Over the Range of User Conditions and Use of thisData to Adjust Recorded Signals from the Dilution Sensor.

As seen from FIG. 7 and FIG. 8, the temperature changes due to insidecooling for a particular catheter construction can be determined bybench studies. From these value of K_(i) as a function of injectate flowrate and the blood flow velocity can be determined. The experimentallydetermined values of K_(i) are used with Equation 13 to estimate S_(c)and thus compensate for the inside cooling effect, or error. The valuesrelated to FIG. 7 and FIG. 8 can be simply determined by placing thecatheter in a bench model of the A-V shunt not facing the blood flow butwith the flow. In this case, the injected indicator (injectate) (such assaline) will cool the dilution sensor 36 from the inside prior toexiting through the ports and will then be flushed away from thecatheter, so the signal recorded by the dilution sensor 36 will berelated only to the inside cooling effect which produces the area curvewith area S_(c). The relationship of FIG. 7 and FIG. 8 will be obtainedby changing the speed of injections and flow rate in the A-V shuntmodel.

The equation for measuring blood flow using such a pre-calibrated sensorfor example for rectangular approximation (FIG. 9 a and Equation 15b)will be from Equation 13: $\begin{matrix}{Q_{f} = \frac{{kV}( {T_{b} - T_{i}} )}{( {S_{m} - {K_{i} \times ( {T_{b} - T_{i}} ) \times t}} )}} & {{Equation}\quad 17}\end{matrix}$

In this expression k, and K_(i) are known from pre-calibration; T_(b),T_(i), S_(m) and t are measured from the dilution curve and injectatesensor, and V is the predetermined volume of injection. The value ofQ_(f) can thus be determined.

2. A Plurality of Injections of Different Volumes or Different TimeLength from which the Inside Cooling Effect on the Thermal DilutionSensor and/or Injectate Temperature can be Calculated.

The area under the measured indicator dilution curve S_(m) is againconsidered to consists of two parts (S_(m)=S_(dil)+S_(c)) (see FIG. 6).The first part (S_(dil)) is produced by the actual blood dilution andfor the same blood flow is proportional to the volume of the injection.The second part, S_(c), is proportional to ΔT_(i) and the length ofinjection, but not to the volume of the injection (injectate) (see FIG.7).

For two injections of different volumes, V_(1 and V) ₂, made atdifferent times, Equation 17 yields, for example for rectangularapproximation, Equation 15b): $\begin{matrix}{Q_{f} = \frac{{kV}_{1}( {T_{b} - T_{i}} )}{( {S_{m1} - {K_{i} \times ( {T_{b} - T_{i}} ) \times {t1}}} )}} & {{Equation}\quad 18a} \\{Q_{f} = \frac{{kV}_{2}( {T_{b} - T_{i}} )}{( {S_{m2} - {K_{i} \times ( {T_{b} - T_{i}} ) \times {t2}}} )}} & {{Equation}\quad 18b}\end{matrix}$

where S_(m1) and S_(m2) are the measured areas under the dilution curvesfrom the first and second injections, respectively, and t1 and t2 arethe length of the first and the second injections, respectively.

In Equations 18a and 18 b the values: S_(m1), S_(m2), t1, t2, and T_(b)are measured from the dilution curves, and the values: V₁, V₂, k, andT_(i) are known. Thus, having two equations with two unknowns, Q_(f) andK_(i), provides that the equations can be solved to measure blood flowQ_(f) with no pre-calibration procedure.

Alternatively, if K_(i) is known from pre-calibrations, but thetemperature of injection T_(i) is unknown (i.e., using a configurationwithout injectate temperature sensor), then again Q_(f) can becalculated from these same equations.

3. A Plurality of Thermal Dilution Sensors where the Magnitude of theDilution Sensor Inside Cooling Effect is Measured by an AdditionalThermal Sensor and Compensated.

The basis of this approach is that the catheter 10 can be designed tohave two or more thermal dilution sensors 36 that are in differentconditions regarding the inside cooling effect and the outside dilutedblood cooling. Readings from these thermal sensors can be compared tocompensate or minimize the inside cooling effect on the accuracy ofblood flow measurement. For example, the catheter 10 can be designedsuch that one sensor is influenced by both inside cooling and blooddilution cooling. The second thermal sensor is influenced dominantlyonly by inside cooling (FIG. 10) with no dead space or with dead space(FIG. 11).

In FIG. 10, the indicator (injectate) passes both thermal sensors fromthe inside of the catheter, but the angled apertures dictating the placewhere the indicator enters the blood stream downstream of the distalthermal sensor 36 b (i.e., the sensor close to the catheter tip) andthus, the signal from the distal thermal sensor is influenced only byinside cooling. If the catheter 10 is designed such that the thermalconductance from the injectate channel is the same for both sensors,then blood flow can be calculated through the difference of thetemperature changes recorded by the two sensors analogous to Equation17. Specifically: $\begin{matrix}{Q_{f} = \frac{{kV}( {T_{b} - T_{i}} )}{( {S_{m\quad p} - S_{d}} )}} & {{Equation}\quad 19}\end{matrix}$

where S_(mp) and S_(d) are the areas under dilution curves from theproximal and distal sensor, respectively.

It may be useful to design the catheter 10 such that the indicatorinjection will introduce turbulence into the channel within catheterand/or the measured blood flow. This turbulence will create circulationin the dead zone (FIG. 11) so that indicator (injectate) will flow alongthe sensing zone of the distal thermal sensor 36 b. This turbulence canbe achieved by changing the angle of apertures of the catheter injectionholes with respect to the main channel, or by introducingdiscontinuities within the injectate lumen for example by creatingspiral ribs 35 within.

An alternative way of compensation is presented in FIG. 12. Here, thecatheter 10 is equipped with two thermal dilution sensors 36 c, 36 d,positioned as shown. The total injected volume of indicator (injectate)V is distributed between the distal injection port with aperture (a×V)and the proximal port(s) with total aperture V(1−a), where “a” is thepercentage or portion of the indicator that leaves the catheter throughthe distal injection port.

The distal thermal dilution sensor 36 d will be cooled by two sources,firstly from the inside, while the volume (a×V) passes; and secondly bythe blood cooled by volume a×V from the outside of the catheter aftermixing with blood: $\begin{matrix}{Q_{f} = \frac{{kV} \times {a( {T_{b} - T_{i}} )}}{( {S_{md} - {K_{id} \times ( {T_{b} - T_{i}} ) \times t_{d}}} )}} & {{Equation}\quad 20}\end{matrix}$

where S_(md) is the total area under dilution curve of the distalthermal sensor. The second part of the sum in denominator is related tothe area under dilution curve on the distal thermal dilution sensor dueto the indicator passing through the lumen inside the catheter; whereindex “d” means distal sensor.

The proximal dilution sensor 36 c will be also cooled by two sources,firstly from the inside while the volume (V) passes; and secondly by theblood cooled by volume V from the outside of the catheter after mixingwith blood:

Both these effects are caused by same total injected volume V.$\begin{matrix}{Q_{f} = \frac{{kV}( {T_{b} - T_{i}} )}{( {S_{mp} - {K_{ip} \times ( {T_{b} - T_{i}} ) \times t_{p}}} )}} & {{Equation}\quad 21}\end{matrix}$

where S_(mp) is the total area under dilution curve of the proximalsensor. The second part of the sum in denominator is related to the areaunder dilution curve on the proximal thermal dilution sensor due to theindicator passing through the lumen inside the catheter; where index “p”means proximal thermal sensor.

Subtracting the temperature readings of these two thermal sensors andconsidering that the inside cooling effect is the same on both sensors,Equations 20 and 21 yield: $\begin{matrix}{Q_{f} = \frac{{{kV}( {1 - a} )}( {T_{b} - T_{i}} )}{( {S_{mp} - S_{md}} )}} & {{Equation}\quad 22}\end{matrix}$

This approach offers the advantage that K_(i) is eliminated from theflow equation; therefore no pre-calibration value K_(i) for both thermalsensors is determined. In practice, if the inside cooling effect is notthe same for these two sensors (making K_(ip) not equal to K_(id)) thisdifference should be considered while combining Equation 21 fromEquation 20.

4. A Plurality of Pre-Calibrated Thermal Sensors, to SimultaneouslyEliminate the Necessity of Measuring the Injectate Temperature and theInside Cooling Effect.

The basis of this approach is that two thermal dilution sensors areemployed in a catheter construction, where the sensors exhibit differentsensitivity to the inside cooling effect from the injectate and theoutside blood dilution cooling. Comparing the data from these thermalsensors helps to eliminate the influence of the injection (injectate)temperature and effect of inside cooling.

Equation 17, and Equation 14 can be written for two thermal sensors “1”and “2”: $\begin{matrix}{Q_{f} = \frac{{kV}( {T_{b} - T_{i}} )}{( {S_{m1} - {K_{i1} \times ( {T_{b} - T_{i}} ) \times t}} )}} & {{Equation}\quad 23a} \\{Q_{f} = \frac{{kV}( {T_{b} - T_{i}} )}{( {S_{m2} - {K_{i2} \times ( {T_{b} - T_{i}} ) \times t}} )}} & {{Equation}\quad 24b}\end{matrix}$

where S_(m1) and S_(m2) are known areas under dilution curves from thefirst and second sensor; K_(i1) and K_(i2) are pre-calibratedcoefficients for first and second thermal sensor respectively (seeEquation 21), (FIG. 7); Solving these equations for Q_(f) yields:$\begin{matrix}{Q_{f} = \frac{{kV}( {S_{m1} - S_{m2}} )}{( {{S_{m2} \times K_{i1}} - {S_{m1} \times K_{i2}}} )}} & {{Equation}\quad 25}\end{matrix}$

As is seen from the above equation, this approach eliminates thenecessity of a separate thermal sensor for injectate temperaturemeasurement.

5. Creating a Special Construction of the Catheter that Will Enhanceand/or Maximize the Thermal Isolation of the Injection Lumen from theThermal Dilution Sensor.

Another way to minimize the influence of the temperature of injectedindicator (injectate) is to thermally separate the injection (injectate)lumen as far as possible from the thermal dilution sensor 36 as seen inFIG. 13. That is, the catheter 10 is constructed to enhance thermalisolation of the thermal sensor from the injectate flowing within thecatheter. Specifically, the conductive heat path can be minimized bylocating a spacer lumen, or gap 42 of relatively high resistance to heatconduction between the injectate lumen and the thermal sensor 36. Theconstruction of the catheter 10 can include a thermal insulating gap asseen in FIGS. 14 a and 14 b that is filled with air, gas or another lowheat conducting material, foam, material having a greater insulationvalue than the material defining the catheter. It is also contemplatedthe insulating gap can include a void holding vacuum. It has been foundthat a significant reduction of the inside-cooling coefficient isobserved for two different catheter geometries. The introduction of anair gap between the distal thermal sensor and indicator (injectate)lumen decreased the K_(i) from K_(i)≈40% at the high blood velocityrates to K_(i)≈4.3%. As set forth, by employing the insulating gap (orlumen), the inside cooling effect from the injectate can still bemeasured and further eliminated by a separate thermal sensor bypre-calibration of the sensor.

A thermal insulating gap such as an inside air lumen can be used toplace the injection (injectate) temperature sensor (FIG. 14) to bethermally proximal to injection (injectate) lumen. In FIG. 14, theinjectate temperature thermal sensor 36 e can accurately measure thetemperature of the injectate. The dilution sensor 36 is locateddownstream of the introduction port to sense the diluted blood flow.Alternatively, (as seen in FIG. 15) the injection temperature thermalsensor 36 e can be located in the same lumen as the distal thermalsensor but the air gap (insulating spacer) can be eliminated, or forexample filled with a thermal conductor such as a plastic, or thematerial of the catheter, to improve heat conductance (FIG. 15) at thelocation of the injection temperature thermal sensor 36 e. The thermalconductor has a greater thermal conductivity than the insulating lumen,and preferably has a thermal conductivity at least as great as thematerial of the catheter.

The thermal isolation is directed to thermally separating the thermaldilution sensor from the indicator (injectate) temperature. Therefore,the present construction is in contrast to the prior constructions of acoaxial catheter which is not retrograde, as the inside catheter wasused to inject indicator that will have maximum isolation from theoutside blood so as not to be heated prior entering blood. That is, inthe prior construction of a coaxial catheter, wherein the entireindicator lumen is thermally spaced from the surrounding blood flow, thepresent catheter thermally isolates the thermal dilution sensor 36 frominjectate flow through the injectate (indicator) lumen, maximizing thethermal resistance between the injectate in the catheter and the thermalsensor. Specifically, in prior coaxial constructions having a radialdimension of the annulus between the injectate and the thermal sensor,the present construction allows effectively twice the radial dimensionof the coaxial construction to be disposed intermediate the injectate inthe catheter and the temperature sensor. That is, the entire crosssectional area of the thermally insulating spacer, gap, is locatedintermediate the injectate lumen and the temperature (thermal dilution)sensor. The present construction allows a reduced catheter crosssectional area with enhanced thermal insulation between the thermaldilution sensor and the injectate lumen, and thus allows the catheter tobe employed with less adverse effect on the measured flow.

For example, the catheter 10 can have an insulating lumen intermediatethe dilution sensor and the injectate lumen. In this construction it isalso possible to locate the injectate temperature sensor within theinsulating lumen, thereby exposing the injectate temperature sensor tothe thermal effect of the injectate passing within the catheter, and thedilution sensor is located to dispose the insulating lumen intermediatethe injectate lumen and the dilution sensor. This creates differingthermal conductive properties between the dilution sensor and theinjectate sensor.

Alternatively, the injectate temperature sensor can be located at aposition spaced from the insulating lumen, wherein a portion of theinsulating lumen includes a thermal conductor to thermally link theinjectate temperature sensor and the injectate lumen.

In a catheter having a generally circular cross section, the thermaldilution sensor is spaced from the injectate lumen by a radius of thecross section. In one configuration, the cross sectional area of thecatheter intermediate the thermal dilution sensor and the injectatelumen is maximized. It is also understood, at least 50% of a crosssectional dimension of the catheter can be located intermediate theinjectate lumen and the thermal sensor, with a preferred constructionproviding at least 70% of catheter cross section dimension being locatedintermediate the thermal dilution sensor and the injectate lumen.However, as much as 90 to 95% of the cross sectional dimension could belocated intermediate the thermal dilution sensor and the injectatelumen.

An alternative construction locates the insulating lumen intermediatethe thermal dilution sensor and the injectate lumen so that along agiven chord of the catheter cross section, the insulating lumen definesa greater portion of the chord than the material of the catheter. In apreferred construction the insulating lumen defines at least 50% of thechord length, with a more preferred construction having the insulatinglumen define at least 75% of the chord length, with a more preferredinsulating lumen defining 80% of the chord length. By increasing thepercentage of a chord length defined by the insulating lumen, thethermal isolation of the thermal dilution sensor can be increased. Thatis, the amount relatively thermally conductive material of the catheteravailable for heat transfer is minimized.

6. Any Combination of the Above.

The accuracy of blood flow measurements by a retrograde catheter bycompensation of inside cooling (or heating) from injectate flow throughthe catheter can be improved by employing any of (i) the precalibrationof the thermal conductive properties of the catheter; (ii) employing aplurality of different injections; (iii) employing a plurality ofdilution sensors; (iv) employing pre-calibrated thermal sensors or (v)thermally isolating the dilution sensor from injectate flowing withinthe catheter.

(ii) Measuring the Temperature of Injected Indicator

In thermodilution measurements of cardiac output, a first distal thermalsensor is located in the pulmonary artery and produces dilution curves,and a second thermal sensor is located in the central vein, in theaperture (or within the aperture) through which indicator solutionenters the blood stream. In this way, the second thermal sensor measuresthe temperature of the solution (injectate) entering the blood. In thepresent case, the existence of multiple small injection ports increasesthe technological difficulty locating a thermal sensor within the spaceof the introduction port. If the thermal sensor is not locatedimmediately near or adjacent the introduction port, the temperature ofthe thermal sensor will be influenced by both the injected indicator(injectate) and the blood temperature, thereby decreasing the accuracyof the resulting measurement.

To solve this problem of measuring T_(i), a second proximal thermalsensor 36 a (FIG. 1, 2) for measuring the temperature of the indicatorinjection (injectate) is located in a part of the catheter 10 that isout of the blood stream. In this case, the temperature of injectedindicator is measured just prior to the indicator entering the part ofthe catheter that is located in the blood stream. The heating/cooling ofthe indicator while passing through the length of the catheter that isin thermal contact with the blood flow of the A-V shunt (before exitingthrough ports into the blood flow) is negligible or can be accounted.Also, the surrounding air has a relatively low thermal conductance (incontrast to the flowing blood) and the thermal sensor 36 a will moreaccurately represent temperature T_(i). It is also noted that the volumeof the indicator injection V must be sufficiently large to besignificantly greater than a priming volume of any liquid contained inthe portion of the injection lumen that is located within the bloodvessel and thus has a temperature that is approximate to the temperatureof the blood.

The thermal sensor 36 a measuring the injection (injectate) temperaturecan be also located out of the body of the catheter 10, such as on thetubing leading to manifold or inside manifold (FIG. 16). Alternatively,the thermal sensor 36 a for measuring the injected indicator can beattached to the tubing line or the catheter 10. The advantage ofattaching the second thermal sensor 36 a out of the body of the catheteris the elimination of the additional lumen for communicating with thesensor. That is, if the sensor 36 a were located inside the catheterbody, the existing lumens would be of a smaller cross sectional area toaccommodate the need for the lumen corresponding to the sensor. Thisallows the catheter to have a smaller cross sectional area and thus canbe used for smaller A-V shunts or smaller other vessels, which may be 6French or less, with less influence on the initial blood flow due to itsmaller size.

Attaching the thermal sensor 36 a (FIG. 16) can reduce the cost of thecatheter, as the attached sensor is not part of a single use catheterand thus can be reusable.

The plastic or catheter material between the injection lumen and theinjection thermal sensor (thermistor) does not reach the temperature ofthe indicator, for some period of time. In some cases, while theoperator is waiting for the injection of the indicator (injectate),blood migrates up through injection channel (lumen) and reaches theinjection thermal sensor and heats the thermal sensor and thesurrounding material of the catheter prior to injection. To minimizethese errors, the minimal temperature is chosen to be T_(i) duringinjection time (taken from the distal sensor in the blood).

In a further configuration, the catheter body includes a thermaldilution sensor lumen, which can receive electrical leads to the thermaldilution sensor as well as the thermal dilution sensor. The catheterbody also includes the injectate lumen and the thermal insulating lumen.The catheter body can include the thermal insulator including a portionof the thermal insulating lumen, thereby effectively receiving acorresponding length of the insulating lumen. The thermal injectatesensor can be located adjacent the thermal conductor to thereby respondto the temperature of the injectate in the injectate lumen. The thermalinjectate sensor can be located in the insulating lumen, the catheterbody or the thermal dilution sensor lumen to be adjacent the thermalinsulator (in the thermal insulating lumen), and thereby provide asignal corresponding to the temperature of the injectate in theinjectate lumen.

1. Thermodilution Catheter Placed with the Blood Flow

Measuring blood flow in the peripheral arteries, such as the kidneyartery requires minimization of the catheter size to eliminate theinfluence on initial blood flow. The relatively large size of acatheter, especially located in the narrowing site of the blood vesselmay decrease the blood flow and introduce inaccuracies intomeasurements. In this situation, it is beneficial to minimize theconstructive elements of the catheter. For example, it is advantageousto use the lumen that is used for the guide wire as a lumen forinjection of the indicator, as seen in FIG. 17. In this situation, partof the introduced injectate volume will exit the catheter 10 downstreamof the thermal sensor and the actual value of V in Equation 1 will bedifferent. To minimize this effect, the lumen at the distal tip of thecatheter can be made narrower than the remaining part of the lumen. Thedistribution of the injected volume V in the particular catheterconstriction can be estimated with prior bench tests. $\begin{matrix}{Q = \frac{{k( {T_{b} - T_{i}} )} \cdot {V( {1 - a} )}}{S}} & {{Equation}\quad 25}\end{matrix}$

where “a” is the portion of indicator that passes from the catheterthrough the distal aperture in the guide wire lumen.

Measurements while the guide wire is inside the catheter 10 willsubstantially reduce the error because the distal aperture will besubstantially blocked by the guide wire. The value of “a” for thissituation must be separately evaluated in the bench studies. Anadditional source of error may appear due to the fact that while theindicator is passing the thermal sensor, the indicator may cool thethermal sensor from inside, thereby introducing error in themeasurements: $\begin{matrix}{Q = \frac{{k( {T_{b} - T_{i}} )} \cdot {V( {1 - a} )}}{( {S_{m} - S_{in}} )}} & {{Equation}\quad 26}\end{matrix}$

where S_(m)—is the total area under the dilution curve; and S_(in)—thepart of the area under dilution curve related to the cooling of thedistal sensor from the inside of the catheter.

While a preferred embodiment of the invention has been shown anddescribed with particularity, it will be appreciated that variouschanges in design and formulas and modifications may suggest themselvesto one having ordinary skill in the art upon being apprised of thepresent invention. It is intended to encompass all such changes andmodifications as fall within the scope and spirit of the appendedclaims.

1. A method of determining blood flow in a conduit, comprisingcompensating for an injectate induced thermal offset of a first thermaldilution sensor connected to a catheter, the injectate induced thermaloffset resulting from travel of the injectate through the catheter, thecompensating including employing a plurality of injections or employinga plurality of thermal sensors.
 2. The method of claim 1, whereincompensating for an injectate induced cooling of a thermal dilutionsensor includes calculating an inside cooling effect on the thermaldilution sensor in response to at least two introductions of injectateinto the conduit.
 3. The method of claim 2, further comprisingintroducing a first injectate having a first volume and introducing asecond injectate having a different second volume.
 4. The method ofclaim 2, further comprising introducing a first injectate over a firsttime and introducing a second injectate over a different second time. 5.The method of claim 1, wherein compensating for an injectate inducedthermal offset of a first thermal dilution sensor includes inducing asecond thermal offset in a second thermal dilution sensor resulting fromtravel of the injectate through the catheter.
 6. The method of claim 1,wherein compensating for an injectate induced thermal offset of a firstthermal dilution thermal sensor includes thermally exposing a seconddilution sensor to a fractional portion of injectate introduced into theconduit.
 7. The method of claim 1, wherein compensating for an injectateinduced thermal offset of a first thermal dilution sensor includeslocating a second thermal dilution sensor relative to one of theinjectate traveling through the catheter and blood flow, to have thermalconductivity properties different from the first thermal dilutionsensor.
 8. A method of determining a blood flow in a conduit, the methodcomprising: (a) sensing a blood parameter related to blood temperature;(b) passing an injectate through a lumen in a catheter, the passinginjectate inducing a measurement offset in a blood parameter sensor; and(c) compensating for the measurement offset of the blood parametersensor by an amount corresponding to one of measurements from aplurality of injections or measurements from a plurality of thermalsensors.
 9. The method of claim 8, wherein compensating for themeasurement offset includes measuring a blood parameter at two spacedapart locations.
 10. The method of claim 8, wherein compensating for themeasurement offset includes introducing a first injectate volume intothe blood flow and introducing a different second injectate volume intothe blood flow.
 11. A method of thermodilution measurement of a bloodflow rate in a conduit, the method comprising compensating for aninjectate induced thermal variance of a thermal dilution sensor, theinduced thermal variance resulting from an injectate flow through acatheter, the compensating including employing a plurality of differentinjections or employing a plurality of thermal sensors.
 12. A method ofdetermining a blood flow by thermodilution measurement, comprising: (a)calculating the blood flow from a measured first dilution curvecorresponding to a first injectate volume having a first injectate timeand a first injectate temperature, and from a measured second dilutioncurve corresponding to a second injectate volume having a secondinjectate temperature and a second injectate time.
 13. A method ofdetermining a blood flow rate by thermodilution measurement, comprising:(a) determining the blood flow rate in response to a temperature of theblood flow, a temperature of an injectate, a volume of the injectate, adilution curve from a proximal thermal dilution sensor and a dilutioncurve from a distal thermal dilution sensor, wherein at least a portionof the injectate is introduced into the blood flow at a location betweenthe proximal thermal dilution sensor and the distal thermal dilutionsensor.
 14. A method of determining a blood flow by thermodilutionmeasurement, the method comprising: (a) exposing a first thermal sensorto a first thermal influence of an injectate flowing in an injectatelumen in a catheter and to a first thermal influence of the blood flowdiluted by the injectate, and (b) exposing a second thermal sensor to adifferent second thermal influence of one of the injectate flowing inthe injectate lumen and the blood flow diluted by the injectate.
 15. Amethod of determining blood flow by thermodilution measurement, themethod comprising: (a) passing a first portion of an injectate volumethrough a first introduction port in a catheter, to combine the firstportion of the injectate with the blood flow thereby forming a firstdiluted flow; (b) thermally sensing the first diluted flow with a firstthermal dilution sensor; (c) passing a balance of the injectate volumethrough at least a second introduction port to combine with the firstdiluted flow to form a second diluted flow; and (d) thermally sensingthe second diluted flow with a second thermal dilution sensor.
 16. Amethod of determining a blood flow rate by thermodilution measurementcomprising: (a) determining the blood flow rate corresponding to afactor representing an amount of an injectate volume passing through aproximal introduction port, a difference between a blood flowtemperature and an injectate temperature, and a difference between anupstream dilution curve obtained upstream of the proximal introductionport and a downstream dilution curve obtained downstream of the proximalintroduction port.
 17. A method of determining blood flow rate bythermodilution measurement with a retrograde catheter, comprising: (a)determining the blood flow rate corresponding to a first dilution curvefrom a first thermal sensor having first thermal conductive properties,and a second dilution curve from a second thermal sensor havingdifferent second thermal conductive properties, and an injectate volume.